The density \(\rho _{ej}\) 
can be converted into particle flux \(F_{ej} = \rho _{ej} \, \langle v \rangle / (4 \pi m)\) 
per steradian, where \(\langle v \rangle \)  is the mean velocity of grains. Motion of micron-sized
grains are affected by solar radiation when entering the Solar System, but
in situ spacecraft measurements indicate that the flux of interstellar
dust grains of \(m \sim 10^{-12} \ \rm g\) 
is not reduced at a distance of about 1 au from the Sun [1]}.
Then the micron-sized
grains from terrestrial exoplanets are accreting on Earth directly from ISM at a rate of
\(A_\oplus = 4 \pi F_{ej} \, \pi \, r_\oplus ^2 \sim 1.6 \times 10^3\)  particles every year,
where \(r_\oplus \)  is the Earth radius. Here, \(m = 10^{-12}\)  g and
\(\langle v \rangle = 40\)  km/s (for the Maxwell distribution
with one-dimensional velocity dispersion \(\sigma _v = 25\)  km/s, [2]})
are adopted, assuming that the grain velocity distribution in ISM is the same as
stars in the solar neighborhood.
